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Check for commutative and associative (Z...

Check for commutative and associative `(ZZ^(+),**)`where `a**b=2^(ab)` for all `a,binZZ`.

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The correct Answer is:
Commutative but not associative
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CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Short Answer Type Questions)
  1. Check for commutative and associative (ZZ,@) where a@b=a+b+ab for all ...

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  2. Discuss the commutativity and associativity ** on RR defined by a**b=|...

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  3. Check for commutative and associative (ZZ^(+),**)where a**b=2^(ab) for...

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  4. Check for commutative and associative ** on RR-{1} defined by a**b=(1)...

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  5. Check for commutative and associative @ on RR defined by x@y = max (x,...

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  6. Discuss the commutativity and associativity(QQ,@) where x@y=(1)/(6)xy...

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  7. Discuss the commutativity and associativity** on RR defined by x**y= m...

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  8. Discuss the commutativity and associativity** on QQ defined bya**b=ab+...

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  9. Discuss commutativity and associativity** on ZZ defined by a**b=a+b+3 ...

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  10. Check for commutative and associative (NN,**) where a**b=gcd(a,b) for ...

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  11. Check for commutativity and associativity ** on ZZ defined by a**b=|a|...

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  12. Discuss the commutativity and Associativity ** on QQ defined by x**y=(...

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  13. Discuss the commutativity and associativity ** on RR defined by a**b=|...

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  14. ** on ZZxxZZ defined by (a,b)**(c,d)=(a-c,b-d) for all (a,b),(c,d)inZZ...

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  15. Check commutativity and associativity @ on M(2)(RR) defined by A@B=(1)...

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  16. An operation ** on ZZ, the set of integers, is defined as, a**b=a-b+ab...

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  17. (I) Let ** be a binary operation defined by a**b=2a+b-3. Find 3**4. ...

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  18. A binary operaiton @ is defined on the set RR-{-1} as x@y=x+y+xy for a...

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  19. If ** be the binary operation on the set ZZ of all integers, defined b...

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  20. A binary operation @ is defined on ZZ, the set of integers, by a@b=|a-...

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